{"title":"Spectral analysis of a coupled bending-torsion beam energy harvester: asymptotic results","authors":"Chris Vales","doi":"10.1016/j.jmaa.2024.129072","DOIUrl":null,"url":null,"abstract":"<div><div>This work is concerned with the spectral analysis of a piezoelectric energy harvesting model based on a coupled bending-torsion beam. After building the problem's operator setting and showing that the governing operator is nonselfadjoint with a purely discrete spectrum, we derive an asymptotic approximation of its spectrum. In doing so, we also prove that the addition of energy harvesting can be viewed as a weak perturbation of the underlying beam dynamics, in the sense that no piezoelectric parameters appear in the spectral approximation's first two orders of magnitude. We conclude by outlining future work based on numerical simulations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"544 2","pages":"Article 129072"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24009946","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This work is concerned with the spectral analysis of a piezoelectric energy harvesting model based on a coupled bending-torsion beam. After building the problem's operator setting and showing that the governing operator is nonselfadjoint with a purely discrete spectrum, we derive an asymptotic approximation of its spectrum. In doing so, we also prove that the addition of energy harvesting can be viewed as a weak perturbation of the underlying beam dynamics, in the sense that no piezoelectric parameters appear in the spectral approximation's first two orders of magnitude. We conclude by outlining future work based on numerical simulations.
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
Papers are sought which employ one or more of the following areas of classical analysis:
• Analytic number theory
• Functional analysis and operator theory
• Real and harmonic analysis
• Complex analysis
• Numerical analysis
• Applied mathematics
• Partial differential equations
• Dynamical systems
• Control and Optimization
• Probability
• Mathematical biology
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• Mathematical physics.